Inverse Boundary Value Problem for Fourth-Order Pseudo-Hyperbolic Equation with Nonlocal Integral Conditions of the Second Kind (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we consider a nonlinear inverse boundary value problem for a fourthorder pseudo hyperbolic equation with nonlocal conditions of the integral type. First, we introduce the definition of a classical solution to the problem. The purpose of this paper is to determine the unknown coefficient of the right-hand side and to solve the problem of interest. The problem is considered in a rectangular domain. To study the solvability of the inverse problem, we perform a transformation from the original problem to some auxiliary inverse problem with trivial boundary conditions. Using the principle of contraction mappings, we prove the existence and uniqueness of solutions to the auxiliary problem. Then we again perform a transformation to the problem and as a result obtain the solvability of the inverse problem.